This package implements bspline and linear interpolation in julia
For most purposes, Interpolations.jl will be preferrable to this package.
However, there are some features which are available here, and not there.
the method getTensorCoef is a very efficient algorithm to compute approximating coefficients from a tensor product of basis matrices. it is efficient because it never forms the tensor product.
the package allows low-level access to objects such as spline knot vectors. Suppose you want to have a knot vector with a knot multiplicity in the interior knot span to approximate a kink. For example,
knots =vcat(lb,-0.5,0,0,0.5,ub)
is a valid knot vector.
Documentation is non-existent. Please look at the tests. Sorry.
Example
using ApproXD
f(x) =abs.(x).^0.5
lb,ub = (-1.0,1.0)
nknots =13
deg =3# standard case: equally spaced knots
params1 =BSpline(nknots,deg,lb,ub)
nevals =5* params1.numKnots # get nBasis < nEvalpoints# myknots with knot multiplicity at 0
myknots =vcat(range(-1,stop =-0.1,length =5),0,0,0, range(0.1,stop =1,length =5))
params2 =BSpline(myknots,deg) # 0: no derivative# get coefficients for each case
eval_points =collect(range(lb,stop = ub,length = nevals))
c1 =getBasis(eval_points,params1) \f(eval_points)
c2 =getBasis(eval_points,params2) \f(eval_points)
# look at errors over entire interval
test_points =collect(range(lb,stop = ub,length =1000));
truth =f(test_points);
p1 =getBasis(test_points,params1) * c1;
p2 =getBasis(test_points,params2) * c2;
e1 = p1 - truth;
e2 = p2 - truth;
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